Although that ruling had been stayed pending the appeal, the appeals-court decision clears the way for President Obama to issue a new proclamation, declaring May 5 as this year’s National Day of Prayer.

The three-judge panel of the Seventh Circuit Court of Appeals in Chicago did not examine the district judge’s legal conclusion that Mr. Obama’s proclamation of a National Day of Prayer and the statute authorizing that action violated the First Amendment’s prohibition on the establishment of a state-sponsored religion.

The Madison, Wis., group was founded in 1976 and seeks to promote strict separation of church and state.

The plaintiffs in the case, said Chief Judge Frank Easterbrook, must be able to show a genuine injury. Feeling excluded or being made to feel unwelcome do not amount to a significant enough injury to confer legal standing to file a constitutional claim against the president, he said.

“Hurt feelings differ from legal injury,” he wrote in the 13-page decision.

The president’s proclamation last year said in part: “I call upon the citizens of our nation to pray, or otherwise give thanks, in accordance with their own faiths and consciences, for our many freedoms and blessings.”

He added: “I invite all people of faith to join me in asking for God’s continued guidance, grace, and protection as we meet the challenges before us.”

Chief Judge Easterbrook said it was “difficult to see how any reader of the 2010 proclamation would feel excluded or unwelcome.”

The proclamation includes the acknowledgment that some Americans prefer to “give thanks” for freedoms and blessings rather than engage in the religious act of prayer.

“Although this proclamation speaks to all citizens, no one is obligated to pray, any more than a person would be obligated to hand over his money if the president asked all citizens to support the Red Cross and other charities,” Easterbrook wrote. “The president has made a request; he has not issued a command. No one is injured by a request that can be declined.”

The decision by Easterbrook and two other judges vacates the decision last April by US District Judge Barbara Crabb. The appeals court remanded the case to Judge Crabb with instructions that it be dismissed.

In her 66-page ruling, Crabb said the proclamation of a National Day of Prayer was unconstitutional because it crossed the line from a mere acknowledgment by government of religion and of things religious. The sole purpose of the proclamation, she said, was to encourage all citizens to engage in prayer.

“In this instance,” she said, “the government has taken sides on a matter that must be left to individual conscience.”

Because the case was resolved on the issue of legal standing, the appeals court did not address the broader constitutional question of where the line must be drawn between church and state.

Instead, the appeals court focused on how much of an injury must be shown before plaintiffs such as the Freedom From Religion Foundation may be granted legal standing.

Easterbrook said it requires more than a feeling of exclusion. But, he said, those who could show they had altered their daily routine to avoid offensive contact with (for example) a religious display on public property would have standing to sue the government.

In contrast, he said, “plaintiffs have not altered their conduct one whit or incurred any cost in time or money. All they have is disagreement with the president’s action.”

Circuit Judge Ann Williams concurred in the decision but wrote a separate opinion. She objected to the appeals court establishing a new rule that limits standing in church-state cases to whether a plaintiff has changed his or her behavior in response to some offending action by the government.

Judge Williams said the US Supreme Court has been less than clear on the issue, but in her view the standing requirement was more permissive than the majority judges had stated.

Nonetheless, she said, the Freedom From Religion Foundation’s allegations in this case were too attenuated to confer standing. She said the allegations seem to amount to nothing more than observing conduct with which they disagree.

The National Day of Prayer was established by Congress in 1952. It has been a tradition since the Truman administration.